This invention relates to methods and apparatus for continuously endowing liquid with mechanical energy by osmosis.
For the sake of clarity the meanings of certain terms as used in this application will be defined. Osmosis involves a semi-permeable membrane, one surface of which is in contact with a first liquid and the opposite surface of which is in contact with a second liquid. The first liquid is a solution relatively more concentrated than the second solution, which latter may be either pure solvent, such as water, or may be a solution in which the solute concentration is less than that in the first solution. The first solution is said to be hypertonic relative to the second solution and may hereinafter be called simply the hypertonic solution. The surface of the membrane in contact with the hypertonic solution may be called the hypertonic surface of the membrane. The region of space containing the hypertonic solution and not including the membrane or the hypertonic surface of the will be designated the hypertonic side of the membrane. Corresponding meanings are used for the terms hypotonic solution, hypotonic surface of the membrane, and hypotonic side of the membrane.
Permeate, a verb, as herein used, means to pass from the region on one side of the membrane through the membrane and out of the membrane into the region on the other side of the membrane. Permeate, a noun, as herein used, means the liquid which permeates.
Concentration polarization is a term used to designate each of two phenomena: (1) the accumulation of a relatively concentrated solution in the vicinity of the hypotonic membrane surface interface by virtue of the osmotic permeation of solvent through the membrane and rejection by the membrane of solute and (2) the accumulation of relatively pure solvent, i.e. relatively dilute solution, in the vicinity of the hypertonic membrane surface interface by virtue of the emergence at that interface of essentially pure solvent permeating the membrane by osmosis. Osmosis will not occur when the concentration at the hypotonic interface equals that at the hypertonic interface. Moreover, as explained hereinafter, osmosis will not occur even when there is some difference in the concentrations at the opposite interfaces of the membrane if the osmotic pressure difference across the membrane due to that difference in concentrations is opposed by a hydrostatic pressure difference of equal magnitude across the membrane.
The mechanical energy with which a liquid can be endowed can be either potential energy or kinetic energy. The potential energy can be either in the form of pressure energy or elevation energy. The kinetic energy is that energy due to the velocity of the liquid. In engineering terms these energies per unit mass of liquid are called pressure head, elevation head, and velocity head.
The classical illustration of osmosis in elementary physics texts shows an inverted thistle tube closed at its larger end with a semi-permeable membrane, the tube containing a quantity of, for example, sugar solution, and the closed end being dipped in a body of, for example, water held in a container. The sugar solution is the hypertonic liquid. The water is the hypotonic liquid. In principle, to enable osmotic flow to occur through the membrane in the direction from the exterior of the thistle tube into the interior of the tube, the water need not be pure but may contain solute so long as the concentration of solute in it is less than that of the sugar solution contained in the tube. Essentially, pure water, the solvent here, flows by osmosis from the body of water in the container into the thistle tube where it rises and, indeed, under some conditions, may flow out of the open end of the thistle tube. If this process in progress is observed, it is seen that the water caused by osmosis to have flowed through the membrane has been endowed with mechanical energy. Choosing strategic locations to observe, the types of energy associated with the water are especially obvious. Those particles of water just entering the interior of the thistle tube at the hypertonic membrane surface interface are quite apparently endowed with pressure energy due to the pressure imposed on them by the weight of the column of liquid existing above them in the thistle tube. Of course they are also endowed with kinetic energy by virtue of the velocity at which they leave the membrane and enter the thistle tube, although this velocity is not so apparent at this location to the observer.
Looking at the free surface of the liquid rising in the thistle tube, or the liquid flowing out of the open end of the thistle tube, as the case may be, it is quite apparent that the permeate is endowed with elevation energy, indicated by the height to which the liquid has risen in the tube, above its initial level, and with kinetic energy, indicated by the velocity with which the liquid is rising in the tube or overflowing out of it.
It is apparent from the foregoing that in order to continuously endow liquid with energy by osmosis, there must be continuous osmotic flow or permeation; that is, continuously liquid must enter an osmotic membrane from the hypotonic side, flow through the membrane, and then flow away from the membrane on the hypertonic side.
Inasmuch as the open end of the thistle tube does not confine the permeate to an enclosed region of space but, on the contrary, allows the permeate to escape and thus flow to any indefinite distance away from the membrane, it might seem, at first blush, that this osmotic process of endowing liquid permeate with mechanical energy could continue indefinitely so long as there was a supply of hypotonic liquid in contact with the hypotonic surface of the membrane.
In fact, this process is discontinuous and will end within a readily foreseeable time interval. In order for osmosis to take place the liquid at the interface with the hypertonic (i.e. downstream) surface of the membrane must always be hypertonic relative to that at the hypotonic (i.e., upstream) surface of the membrane. The functional relation between the osmotic flow through the membrane and the relative tonicities of these two liquids will be apparent from the following.
The rate of permeation of the liquid through such an osmotic membrane is given by dQ/dt=KA(.DELTA.P-.DELTA..pi.), where dQ is the quantity of water transported in time dt; A is the area of the membrane; .DELTA.P=P.sub.o -P.sub.r, where P.sub.o is the hydrostatic pressure on the exterior (hypotonic) surface of the membrane and P.sub.r the hydrostatic pressure on the interior (hypertonic) surface of the membrane; and .DELTA..pi.=.pi..sub.o -.pi..sub.r, where .pi..sub.r is the osmotic pressure of the liquid in contact with the interior (hypertonic) surface of the membrane and .pi..sub.o is the osmotic pressure of the liquid in contact with the exterior (hypotonic) side of the membrane. The osmotic pressure of each liquid is a monotonic increasing function of the concentration of solute in the liquid.
Assuming that the overflow from the thistle tube is conducted away from the container in which the tube is immersed so that the overflow does not mix with the liquid in the container, it is apparent from the foregoing equation that flow through the membrane will cease as soon as the liquid in the thistle tube in contact with the hypertonic surface of the membrane exhibits such a concentration, i.e. such a state of dilution, that its osmotic pressure has a value such that .DELTA..pi. just equals the then-existing .DELTA.P.
As previously stated, the permeate is essentially pure water. As this pure water emerges from the membrane on the hypertonic side it constitutes, at the moment of emergence, the liquid in contact with the hypertonic surface of the membrane. If it were to form a residual, essentially stagnant layer at the hypertonic interface, then osmosis would thereupon cease because there would then be zero difference in concentrations and hence in osmotic pressure between the liquids in contact with the opposite surfaces of the membrane. Since osmotic permeation is not a turbulent flow, such a stagnant layer does tend to form in the absence of the provision of some force to cause rapid mixing of the permeate with the body of hypertonic liquid. No such force exists in the thistle tube apparatus.
The only source for hypertonicity on the hypertonic side of the membrane is the discrete, unreplenished body of hypertonic solution initially installed in the thistle tube. The permeate dilutes this discrete body of liquid which initially, in its undiluted state, and thereafter in its diluted states, contitutes the entire bulk of the solution located on the hypertonic side of the membrane at all significant times and at such a place as conceivably to be capable of participating in osmosis through the membrane. Osmotic flow will cease when the dilution reduces the osmotic pressure of the hypertonic liquid to the extent that the difference, .DELTA..pi., of osmotic pressures at the two interfaces of the membrane no longer exceeds the hydrostatic pressure difference across the membrane.
Other pertinent prior art is illustrated by U.S. Pat. No. 3,423,310. This patent shows a direct osmosis cell having, in effect, two compartments separated by an osmotic membrane, one of the compartments capable of being supplied essentially continuously with a hypotonic solution, and the other compartment being supplied prior to initiation of osmosis with a discrete body of hypertonic liquid and, during osmosis, being essentially sealed to prevent influx of any additional hypertonic liquid and being operated so as, in effect, to prevent efflux from the compartment of permeate originating from the hypotonic solution and emerging from the membrane into the hypertonic compartment. All the elements constituting the boundaries of the hypertonic-liquid-containing compartment are essentially rigid and immovable with the exception of one. That one is formed to be capable of transmitting pressure from the hypertonic liquid in the direct osmosis cell to hypertonic liquid in a reverse osmosis cell to be powered by the energy with which the permeate in the direct osmosis cell is endowed. That element is also so formed and installed that, in coaction with the structure and operating characteristics of the other components of the direct osmosis cell it is capable of being displaced, at least in part, over a limited distance so as to transmit pressure to, and remain in pressure-transmitting relation over that limited displacement with, a surface of the hypertonic liquid in the reverse osmosis cell as that surface recedes by virtue of efflux of permeate from the reverse osmosis cell in response to the pressure exerted by the pressure-transmitting element. The pressure-transmitting element is exemplified variously in the patent by an elastic, liquid-tight diaphragm; a piston of liquid immiscible with the two hypertonic liquids; a gas piston; a solid, rigid, free piston; and an interface between the two hypertonic liquids which is established by, and whose integrity is maintained by, respectively, initially positioning the denser of the two liquids below the other and operating the cell so as to minimize mixing.
The process of the aforementioned Popper patent is discontinuous. That is, the process can proceed for only a clearly limited time interval and will then cease. For one thing, even assuming that there is constantly maintained across the direct osmosis cell membrane a favorable osmotic pressure difference tending to drive permeate from the hypotonic side thereof through that membrane to the hypertonic side thereof, the permeate cannot continuously flow away from the hypertonic side. Ultimately the flow away from the hypertonic side would cease when the hypertonic compartment, which is of finite volume, become full. It can be said to be full when the displaceable boundary element (whose displacement contributes to the total available finite volume of the hypertonic compartment) has, by the influx into the hypertonic compartment of permeate, been displaced to such an extent that, by virtue of either external force on it, or the stress developed in its material, the resistance it exhibits to further displacement balances the force tending to drive additional permeate through the osmotic membrane.
In actual practice the osmotic flow will cease even sooner than suggested by the foregoing analysis. The patent itself, indicates that, as its operation proceeds, the liquid in the hypertonic compartment of the direct osmosis cell becomes dilute and therefore the osmotic pressure difference across the direct osmosis membrane, which is what drives the permeate through the membrane, is reduced. As is apparent from the flow rate equation previously set forth, the flow through the direct osmosis membrane will cease, and hence also will the endowing of the permeate with energy, when the hydrostatic pressure built up in the hypertonic compartment and opposing osmotic flow just equals the then existing osmotic pressure difference across the membrane.